Algae is introduced by water and can grow in diesel fuel.
Drain and clean the tank if the problem is bad.
If the car is prior to the common rail injection systems - say, pre '90
I'd add a couple of gallons of REGULAR (low octane) gasoline to about
1/2 tank of diesel. Yes gas. The motor will be somewhat depowered and
clatter more than normal but the gas will kill the algae.
Alternatively, Biocides are sold for commercial use by various companies
- do a Google on Biocides and you'll have those brands. Not cheap.
Either way, you're going to get some (more) practice changing filters.